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Given algebraic expressions for 3 consecutive terms of an arithmetic sequence, find various values. Same again for a geometric sequence. Instructional exercise consisting of question 11 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given ...

Find the maximum values of two transformations of a function. This is an instructional exercise consisting of question 11 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked ...

Use the binomial expansion of a power of a complex number to find unknown constants. Instructional exercise consisting of question 7 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked ...

Use mathematical induction to prove the result for a given summation. Instructional exercise consisting of question 10 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each ...

Differentiate a product and a quotient. Instructional exercise consisting of question 1 from Paper 1 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each part of the question. Including ...

Determine if two lines are perpendicular to each other. This is an instructional exercise consisting of question 4 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to ...

Carry out an integration using integration by parts. Instructional exercise consisting of question 3 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each part of the ...

Find the integral of a trigonometric expression. This is an instructional exercise consisting of question 7 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each ...

Use the Euclidean algorithm to solve a given Diophantine equation. Instructional exercise consisting of question 2 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each part ...

Find the area enclosed between two given curves. This is an instructional exercise consisting of question 9 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each ...

Integrate an expression involving the power of a linear expression. This is an instructional exercise consisting of question 2 from the second paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked ...

Prove a given trig identity, and use it to integrate a given derivative back to the original equation. This is an instructional exercise consisting of question 10 from the second paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in ...

Find the particular solution to a linear first order differential equation given initial values. Instructional exercise consisting of question 6 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the ...

Evaluate the scalar product of a vector with the sum of two vectors. This is an instructional exercise consisting of question 14 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the ...

Solve a trigonometric involving the sine of a linear function. This is an instructional exercise consisting of question 8 from the second paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked ...

Finding the equation of a plane given 3 points on it. Finding the equation of a parallel plane. Finding the equation of a line. Finding the point of intersection of a line and a plane. Instructional exercise consisting of question 12 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative ...

Express a given rational expression in partial fractions. Use this to solve a given differential equation modeling a population growth. Instructional exercise consisting of question 9 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given ...

Find the particular solution of a given second order differential equation. Instructional exercise consisting of question 8 from Paper 1 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to ...

Express a power of a matrix as a linear combination of itself and I. Find a similar result for the inverse of the matrix. Instructional exercise consisting of question 5 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in ...

Find the equation of the tangent to a curve given by parametric equations at a given point. Instructional exercise consisting of question 4 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the ...

Finding the complex roots of a given equations, given the first root. Deriving a given result from the sum of the roots. Instructional exercise consisting of question 13 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in ...

2022 National 5 Applications Of Maths Exam Paper 1 Full Solutions gives the official SQA marks for the 2021 National 5 Applications Of Mathematics Exam Paper. This Video will cover the whole of 2021 National 5 Applications Of Maths Paper 2 with full official solutions. https://maths.scot/pdf/n5apps/SQA/N5_Applications-of-Mathematics_all_2021 ...

1. Calculate the magnitude of a vector in 3D given its components . 2. Subtract two given mixed numbers. 3. Expand and simplify an expression involving the sum of the products of expressions. Instructional exercise consisting of questions 1, 2 & 3 from the first paper of the 2021 SQA National 5 Mathematics resource paper. Where appropriate the ...

10. Create and use a linear equation to model the connection between wages and sales. 11. Solve a linear inequation. 12. Find the original value from a given percentage of it. Instructional exercise consisting of questions 10, 11 and 12 from the first paper of the 2021 SQA National 5 Mathematics resource paper. Where appropriate the alternative ...

Fully factorise a given cubic expression. This is an instructional exercise consisting of question 10 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each part of ...

Find the asymptotes of a given ration function and sketch its graph. Instructional exercise consisting of question 7 from Paper 1 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each ...

Find the value of the cosine of the sum of two angles from a diagram involving two right angled triangles. This is an instructional exercise consisting of question 5 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in ...

Given an expression for the velocity of a particle, find an expression for its displacement. Calculate the acceleration at a given time. Instructional exercise consisting of question 6 from Paper 1 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given ...

Find the equation of the inverse of a given function. This is an instructional exercise consisting of question 3 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to ...

Use Gaussian elimination to find the value of an unknown constant in a system of equations. Instructional exercise consisting of question 4 from Paper 1 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the ...

Find the equation of a line given a point and its angle to the x-axis. This is an instructional exercise consisting of question 8 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the ...

Find a product, transpose and inverse, given two matrices. Instructional exercise consisting of question 2 from Paper 1 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each part of the ...

16. Calculate a length involving the distance of a chord to the centre. 17. Solve a given quadratic equation. Instructional exercise consisting of questions 16 and 17 from the first paper of the 2021 SQA National 5 Mathematics resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of ...

Find the volume of a solid formed by rotating a given curve about the x-axis. Instructional exercise consisting of question 5 from Paper 1 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to ...

Find the derivative of an implicit equation and show that there is only one stationary point on the curve. Instructional exercise consisting of question 8 from Paper 2 of the 2021 SQA Advanced Higher Mathematics assessment resource. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then ...

Find the equation of the tangent to a given curve at a given point. This is an instructional exercise consisting of question 1 from the second paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked ...

Find the value of the derivative of a given function involving a power of a quadratic expression. This is an instructional exercise consisting of question 2 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages ...

1. Find an expected price after two years. 2. Carry out a calculation involving numbers in scientific notation. 3. Factorise an expression involving a difference of squares . Instructional exercise consisting of questions 1, 2 and 3 from the second paper of the 2021 SQA National 5 Mathematics resource paper. Where appropriate the alternative ...

Find the coordinates of one of three collinear points in 3D space given the other two and the magnitude of one line segment. This is an instructional exercise consisting of question 12 from the first paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are ...

4. Calculate the size of an angle in a given scalene triangle. 5. find the components of a resultant vector from a diagram of two vectors. Instructional exercise consisting of questions 4 and 5 from the second paper of the 2021 SQA National 5 Mathematics resource paper. Where appropriate the alternative methods for solving the problem are also ...

Find the coordinates of the points where a given line intersects a given circle. This is an instructional exercise consisting of question 15 from the second paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then ...

8. Find the area of a segment in a circle. 9. find the gradient and y intercept of a line. 10. Change the subject of a formula involving a square root. Instructional exercise consisting of questions 8, 9 and 10 from the second paper of the 2021 SQA National 5 Mathematics resource paper. Where appropriate the alternative methods for solving the ...

18. Calculate a length involving the distance of a chord in a circle to the centre. 19. Solve a given quadratic equation. Instructional exercise consisting of questions 18 & 19 from the first paper of the 2021 SQA National 5 Mathematics resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in ...

Derive a given equation from given information, and find the value of its variable for the minimum value. This is an instructional exercise consisting of question 9 from the second paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in ...

Find the components of various resultant vectors in a 3D wire prism. This is an instructional exercise consisting of question 13 from the second paper of the 2021 SQA New Higher Mathematics examination resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the ...

6. Find the mean and standard deviation of a set of six numbers, and compare them to a similar set. 7. Find the length of one side of a triangle given the other two lengths and their bearings. Instructional exercise consisting of questions 6 and 7 from the second paper of the 2021 SQA National 5 Mathematics resource paper. Where appropriate the ...

11. Find the volume of a cone given its slant height. 12. Divide two fractions involving expressions. Instructional exercise consisting of questions 11 and 12 from the second paper of the 2021 SQA National 5 Mathematics resource paper. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try ...

A complete walk through of AQA GCSE Maths 2021 Higher Tier - Paper 1 non-calculator (Originally intended as June 2021 paper set, but cancelled due to Covid and is now listed on the AQA website as November 2021). Help revise for the new specification 9-1 mathematics exams and your mock. This walkthrough tutorial has full solutions to each ...

This is quite long as three different methods are used to obtain the factorization needed to solve a given cubic equation. This is an instructional exercise consisting of question 13 from the first paper of the 2022 SQA New Higher Mathematics examination. Where appropriate the alternative methods for solving the problem are also given. Set out ...

Evaluate the derivative of a trigonometric function. This is an instructional exercise consisting of question 12 from the first paper of the 2022 SQA New Higher Mathematics examination. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each part of the ...