WJEC A‑Level Maths questions by topic

Summer 2025 Unit 3, question 1: 1. (a) Differentiate each of the following functions with respect to x.   3 e x 2   x (i) [2] 2 x e sin3 x (ii) [3] cos2 x (iii) [3] 2 x  1 (b) A function

Summer 2025 Unit 3, question 2: 2. (a) Find all values of x in the range 0XxX2π satisfying the equation cos2 sin 0 x  x  . Give your answers in terms of π. [6] Find all values of θ in the ra

Summer 2025 Unit 3, question 3: cos  Given that θ is small, find an estimate for the solution of the equation  0 8  3. . 1 sin 2  [6]

Summer 2025 Unit 3, question 4:  2 sec x x d 4. (a) Using the trapezium rule with 5 ordinates, find an approximate value for . 0 Show your working and give your answer correct to three decima

Summer 2025 Unit 3, question 5: 2 f x ( )  x  6 x  12 x  . 5 5. A curve is defined by (a) Find the coordinates of the stationary point and determine its nature. [6] Determine the range of

Summer 2025 Unit 3, question 6: ex y  6. The diagram below shows a sketch of the curve with equation and the straight line with y  3 x equation . y x O The straight line intersects the curve

Summer 2025 Unit 3, question 7: 7. The first and last terms of an arithmetic series are –3 and 61 respectively. The sum of all of the terms is 957. Determine (a) the number of terms, [2] (b) t

Summer 2025 Unit 3, question 8: 3 2 x  5 x  7 x  29 x  30 By algebraic division, or otherwise, simplify the expression . [5] 8. 3( 5)( 3)( 2) x  x  x 

Summer 2025 Unit 3, question 9: Use proof by contradiction to show that there are no integers x and y for which 3 x  15 y  2 9. . [4]

Summer 2025 Unit 3, question 10: . for 0 X xX α, where 0 ~ α ~ 2 y sec x  10. (a) Sketch the graph of [1]   sec d x x   (b) Explain why . [2] 0

Summer 2025 Unit 3, question 11:  5 2 x  d x 11. Find , giving your answer in the form lna + b, where a, b are constants.   2  1 2 1 x  x  [10] 1

Summer 2025 Unit 3, question 12:  x in ascending powers of x up to and including the term in x3. 12. Expand 3 1 2  x State the range of values of x for which the expansion is valid. [7]

Summer 2025 Unit 3, question 13: 13. A curve is defined parametrically by 2 3 1 y 3 t 2 x  t  ,  . Show that the gradient of the curve at the point with parameter p is 1 (a) p . [4] t  . 1

Summer 2025 Unit 3, question 14:  2 x cos d x x 14. (a) Use integration by parts to find the exact value of . [6] 0  ln x d x u  1 ln x . (b) Use the substitution to find [5]   2 x 1 ln 

Summer 2025 Unit 3, question 15:  f x  , where x ` 3. 15. A function f is defined by 2   x  3 (a) Determine the range of f. [2] f  1( ) x (b) Find an expression for . [5]

Summer 2025 Unit 3, question 16: 16. A person borrows £50 000 which is to be repaid over 20 years in 20 equal annual amounts. The lender charges an annual compound interest rate of 5% which rem