algebra core p1
TRANSCRIPT
For
Examiner's
Use
1 Solve the simultaneous equations. 4x + y = 18 5x + 3y = 19
Answer x =
y = [3]
2 Solve the simultaneous equations. 6x + 2y = 22 4x − y = 3
Answer x =
y = [3]
3 w = 3a – 5b
Calculate w when a = 2 and b = –3.
Answer w = [2]
1
For
Examiner's
Use
4 Solve the equation 4x – 2 = 7 .
Answer x = [2]
5 Solve the simultaneous equations. 3x + 5y = 24 x + 7y = 56
Answer x =
y = [3]
2
6 Simplify the expression.
7x + 11y + x – 6y
Answer [2]
For
Examiner's
Use
7 Solve the simultaneous equations. x + 5y = 22 x + 3y = 12
Answer x =
y = [2]
3
8 Solve the equation.
2
32 −x
= 2
Answer x = [2]
9 Factorise completely.
5g2h + 10hj
Answer [2]
For
Examiner's
Use
10 (a) Factorise xy – y2.
Answer(a) [1]
(b) Solve 4x − 7 = 12.
Answer(b) x = [2]
11 (a) Simplify 4p + 3q + 5p –7q.
Answer(a) [2]
(b) Make x the subject of this formula. g = 2x + y
Answer(b) x = [2]
4
12 (a) Write down all the factors of 15.
Answer(a) [1]
(b) Factorise completely. 15p2 + 24pt
Answer(b) [2]
For
Examiner's
Use
13 (a) Solve the equation 5(x − 3) = 21 .
Answer(a) x = [2]
(b) Make x the subject of the equation y = 3x − 2 .
Answer(b) x = [2]
14 (a) Find the value of 7p – 3q when p = 8 and q = O5 .
Answer(a) [2]
(b) Factorise completely. 3uv + 9vw
Answer(b) [2]
5
15 Make p the subject of the formula m = p2 − 2.
Answer p = [2]
For
Examiner's
Use
16 Solve these simultaneous equations.
5x – 2y = 17 2x + y = 5
Answer x =
y = [3]
17 (a) Expand and simplify.
2(3x – 2) + 3(x – 2)
Answer(a) [2]
(b) Expand. x(2x2 – 3)
Answer(b) [2]
6
For
Examiner's
Use
18 Expand the following expressions.
(a) 5(3 – 4h)
Answer(a) [1]
(b) )22
6(4 edd +
Answer(b) [2]
19 Simplify the following expressions.
(a) 6r + 2s + s – 4r
Answer(a) [1]
(b) 4f 2 – 3g + 4g – 9f
2
Answer(b) [2]
20 Factorise completely 6mp − 9pq.
Answer [2]
7
For
Examiner's
Use
21 Solve the simultaneous equations.
3x + y = 19 5x – y = 13
Answer x =
y = [3]
22 When c = 10 and d = −2, find the value of the following expressions.
(a) c + 2d
Answer(a) [1]
(b) 5c2 − cd
Answer(b) [2]
23 Solve the simultaneous equations.
3x − 2y = 15 2x + y = 17
Answer x =
y = [3]
8
For
Examiner's
Use
24 Solve the simultaneous equations.
2x − y = 9
7x + 2y = 26
Answer x =
y = [3]
25 (a) Factorise 2
3 7y xy− .
Answer(a) [1]
(b) Expand the brackets and simplify completely.
( ) ( )4 5 2 6p p r r p r+ + +
Answer(b) [3]
26 Factorise completely. 2xy – 4yz
Answer [2]
27 Make x the subject of the formula. 53+=
xy
Answer x = [2]
9
For
Examiner's
Use
28 Solve the simultaneous equations. x + 2y = 3
2x – 3y = 13
Answer x =
y = [3]
29 (a) Expand the brackets and simplify.
3(2x O 5y) O 4(x O y)
Answer(a) [2]
(b) Factorise completely.
6x2O 9xy
Answer(b) [2]
30 Solve the simultaneous equations. 3x + y = 30 2x – 3y = 53
Answer x =
y = [3]
10
For
Examiner's
Use
31 Solve the simultaneous equations
5x −3y = 3,
6x − y = 14.
Answer x =
y = [3]
32 J = 3
md
(a) Find the value of d when J = 32 and m = 8.
Answer(a) d = [2]
(b) Make d the subject of the formula.
Answer(b) d = [2]
33 Expand the brackets and simplify 3x − 5(4x − 2).
Answer [2]
11
For
Examiner's
Use
34 (a) Factorise 3mp + 7p2.
Answer (a) [1]
(b) Simplify completely 8(3m + p) − 5(2m − 3p).
Answer (b) [3]
35 (a) Expand and simplify 4(5c – 3d) – 7c.
Answer(a) [2]
(b) Factorise m2 – mn.
Answer(b) [1]
36 Solve the equation 5x + 1 = 54.
Answer x = [2]
12
For
Examiner's
Use
37 z = 2x – y
(a) Find z when x = –3 and y = 7.
Answer(a) z = [1]
(b) Make x the subject of the formula.
Answer(b) x = [2]
38 Factorise completely 6x − 9x2y.
Answer [2]
39 (a) When x = −4 and y = 6, find the value of
(i) x3,
Answer(a)(i) [1]
(ii) xy2.
Answer(a)(ii) [1]
(b) Simplify 1
2
z
z
−
−
.
Answer(b) [1]
13
For
Examiner's
Use
40 Solve the equation 2 – 3x = x + 10.
Answer x = [2]
41 Factorise completely 2pq – 4q.
Answer [2]
42 Expand the brackets and simplify
4x2 – x(x −2y).
Answer [2]
43 The formula for the perimeter, P, of a rectangle with length a and width b is
P = 2a + 2b. Make a the subject of the formula.
Answer a = [2]
14
For
Examiner's
Use
44 Factorise completely 2a2b − 6a.
Answer [2]
45 The surface area of a sphere with radius r is A = 4πr2.
(a) Calculate the surface area of a sphere with a radius of 5 centimetres.
Answer(a) cm2 [1]
(b) Make r the subject of the formula A = 4πr2.
Answer(b) r = [2]
46 Factorise completely 2x2 – 6xy.
Answer [2]
47 Solve the simultaneous equations 3x − y = 18, 2x + y = 7.
Answer x =
y = [3]
48 Factorise 3xy – 2x.
Answer [1]
49 Solve the equation 5x – 7 = 8.
Answer x = [2]
15
For
Examiner's
Use
50 Solve the equation 5x − 2 = 10x − 8.
Answer x = [2]
51 When x = –3 find the value of
x3+ 2x2.
Answer [2]
52 Make s the subject of the formula p = st – q.
Answer s = [2]
53 (a) Expand the bracket and simplify the expression
7x + 5 – 3(x – 4).
Answer (a) [2]
(b) Factorise 5x2 – 7x.
Answer (b) [1]
16
54 When x = 5 find the value of
(a) 4x2,
Answer(a) [1]
(b) (4x)2.
Answer(b) [1]
55 Factorise completely xzxy 64 � .
Answer [2]