1.
Expand and simplify 3(x + 4) + 2(x − 1). [2]
JD SCIENCE
Algebra
Answer all questions. Show working. Answers are in a separate file on the Worksheets page — do not look at them until you have finished.
2.
Expand (x + 5)(x + 4). [2]
3.
Factorise x² + 9x + 20. [2]
4.
Factorise fully 6x² + 9x. [2]
5.
Solve 5x − 4 = 22. [2]
6.
Solve 5x + 7 = 7x − 3. [3]
7.
Solve the inequality 2x + 1 < 13.
(a) Solve the inequality. [2]
(b) Represent the solution on a number line. [1]
8.
Solve the simultaneous equations: y = 2x + 1 and 3x + y = 13. [3]
9.
Solve x² − 5x + 6 = 0. [3]
10.
Solve x² + 4x − 2 = 0. Give answers in surd form. [3]
11.
Complete the square for x² + 6x + 5. [3]
12.
The nth term of a sequence is 5n + 4. Find the first 3 terms and the 20th term. [3]
13.
Here is a sequence: 5, 8, 11, 14, … Find the nth term. [2]
14.
Rearrange v = u + at to make t the subject. [2]
15.
Rearrange A = 2πr(r + h) to make h the subject. [3]
16.
Simplify (3x²y)³. [2]
17.
Simplify (8x⁶)¹/³. [2]
18.
f(x) = 5x − 1. Find f(4) and f⁻¹(x). [3]
19.
Solve 2^{x} = 32. [2]
20.
The line L has gradient 5 and passes through (0, 4). Write the equation of L. [2]
21.
Find the equation of the line through (2, 7) and (6, 15). [3]
22.
Expand (2x − 3)². [2]
23.
Simplify (x² − 9)/(x − 3), x ≠ 3. [2]
24.
Grace solves 3(x − 2) = 12 and writes x − 2 = 12, so x = 14.
(a) Explain the mistake. [1]
(b) Work out the correct solution. [2]
25.
Solve |2x − 1| = 7. [3]
26.
The quadratic graph y = x² − 4x + 3 crosses the x-axis at A and B. Find the coordinates of A and B. [3]
27.
Sketch y = (x + 2)(x − 4), showing intercepts. [4]
28.
Work out the 5th triangular number and show that the nth triangular number is n(n + 1)/2 for n = 5. [2]
29.
Solve 4x² = 64. [2]
30.
If p is directly proportional to q and p = 7 when q = 2, find p when q = 8. [3]
31.
Simplify 2(x + 6) − (x − 6). [2]
32.
On a OCR paper, a 3-mark algebra question usually needs a method mark. Write two things an examiner looks for when you solve a quadratic. [2]