Year 11 Revision#1
7) Simplify the following.
1) Express 123.456 correct to
(a) 2 significant figures
(b) 2 decimal places
12a 2b
(a)
15ab3
2) Evaluate 0.2 × 0.006.
(b)
3) By writing each number correct to one significant figure,
estimate the value of
2 p 2 5q
´
(c)
15q3 8 p
58.7 × 4.08
19.7!
4) Write the number 0.05042 correct to 3 significant figures.
5) By making suitable approximations, estimate the value of
√".$% ×()*."
*.$%+
Show clearly the approximations you use.
6) Expand and simplify.
(a) 3( x + 1) - 5 x
(b) 5(a + 7) + 2(a + 4)
(c)
(2 x + 3)( x - 1)
(d)
3x - 9
6 x + 15
!"!
#$%
&"
÷ '($
(e)
x 2y
+
3 5
(f)
4
1
6 p 3p
(g)
4
3
y -3 y +5
8) Solve simultaneously
(a) 3x + 4y =13
2x – y = 13
(b) 3x + 2y = 5
x–y=5
9) p= 5 x 109 q= 9 x 10-16 Expressing the answer in standard form,
find
(a) p x q
(b) +𝑞
−1 1
10) P = (3 4 −5) , Q = ' 1
0 *.
0 −1
Find PQ.
−1 −3
1 −2
11) (a) Express as a single matrix +
,− +
, .
1
0
2 −5
1 −1
(b) Find the inverse of +
,.
5 3
12) (a) Express as a single matrix
1 3
4 0
3+
,− +
,
−2 5
−1 2
3 −2
(b) A = /
The determinant of A is 2 .
𝑝 −11
(i) Find p.
(ii) Find A-1 .
13) A café sells hot drinks. On Monday it sells 80 teas, 60 coffees and 40 hot
chocolates. On Tuesday it sells 70 teas, 90 coffees and 50 hot
chocolates. A cup of tea costs $0.80, a cup of coffee costs $1 and a cup
of hot chocolate costs $1.20. This information can be represented by
the matrices M and N below.
0.8
80 60 40
M=+
, N=' 1 *
70 90 50
1.2
(a) Work out MN.
(b) Explain what the numbers in your answer represent.
𝑥
−2
4
14) Find the values of x and y, where 2+ , = 3/ 1 - + ,
𝑦
7
−2
𝑥
3 −1 0 11
4
15) +
, ' * = + , , Find x and y.
1 0 1
9
𝑦
[2]
1 −1
0 3
, B = 9! 0 :
−1 𝑥
"
(a) Express 2A −3B in terms of x.
16) A = +
(b) Given that A= B−1 , find the value of x.
17) Answer the whole of this question on a sheet of graph paper.
The rhombus ABCD has vertices A(2, -6), B(5, -5), C(6, -2) and D(3, -3).
(a) Using a scale of 1cm to represent 1 unit on each axis, draw the x
and y axes for −6 ≤ 𝑥 ≤ 6 and −10 ≤ 𝑦 ≤ 6 . Draw and label the
rhombus ABCD.
(b) A reflection in the x-axis maps ABCD onto A1B1C1D1.
Draw and label A1B1C1D1.
(c) The vertices of the rhombus A2B2C2D2 are A2(-6, -2), B2(-5, -5), C2(2, -6) and D2(-3, -3).
(i) Draw and label triangle A2B2C2D2 .
(ii) Describe fully the transformation which maps ABCD onto
A2B2C2D2 .
18) Answer the whole of this question on a sheet of graph paper.
Using a scale of 1cm to represent 1 unit for both axes, draw the x and y
axes for −10 ≤ 𝑥 ≤ 8 and −8 ≤ 𝑦 ≤ 12 .
(a) Draw the triangle with vertices (3, 0), (3, 2) and (1, 1) and label it as
X.
(b) A transformation M maps X onto triangle Y and vertices. (-3, 0),
(-3, 6) and (-9, 3).
(i) Draw and label triangle Y.
(ii) Describe fully the transformation M.
1
20
19)
𝑘 5
22) (a) The determinant of the matrix +
, is 14. Find k.
−1 2
y
7
6
(b) Find the inverse of the matrix +
5
C
4
3
1
–8 –7 –6 –5 –4 –3 –2 –1 0
–1
1
2
3
2 −4
,.
1 3
(a) Calculate the value of the determinant of A, |𝐴|.
(b) Write down 𝐴#! .
(c) Using the information from (b), solve the following using matrix
method.
2𝑥 − 4𝑦 = 10
𝑥 + 3𝑦 = −5
23) Given that matrix 𝐴 = +
A
2
3 −1
,.
−4 2
4
5
6
7
8
–2
x
–3
–4
–5
B
–6
–7
24) 𝐴 = +
2
2 3
3
1
,, 𝐵 = +
,, 𝐶 = (1 2 3), 𝐷 = ' 1 *
−1 0
−4 −3
−1
Find
(a) 𝐴 − 𝐵
(b) 𝐴$
(a) Describe fully the single transformation that maps triangle A onto
7
(c) 𝐴𝐴#! + ,
triangle B.
8
(d)
𝐶𝐷
(b) Triangle A is mapped onto triangle C by the single transformation H.
.....................................................................................................................................................
[2]
Find the matrix representing H.
−2𝑝 3𝑝
1 −3
−1 0
(c) ATransformation
M is a reflection
in thetransformation
line x = 2. Transformation
R
25) 𝐴 = +
,
𝐵=/
𝐶=+
,
1
(b) Triangle
is mapped onto triangle
C by the single
H.
−3𝑝
𝑝
3 −2
0 1
is a rotation 180° about (0, 0).
(a) Evaluate 𝟒𝐂 − 𝟐𝐀.
Find the matrix
representing
H. onto triangle D such that RM(A)=D.
Triangle
A is mapped
(b) Given that 𝐁 = 𝐀#𝟏 , find the value of p.
Draw and label triangle D.
(c) Find the 2 × 2 matrix X, where 𝐀𝐗 = 𝐂.
(d) The matrix C represents the single transformation T.
20) Evaluate
f
p [2] Describe, fully, the transformation T.
2
1
0 4
(a) 3'4* − 2 ' 6 *
(b) (1 3 4) '3 1*
26) The coordinates P (3, 2), Q (3, 4), and R (6, 2) represent a Triangle A
(c) Transformation
reflection in the line x = 2.
0 M is a −3
5 0
0 −1
which is under transformation of reflection 𝑀 = +
,.
Transformation R is a rotation 180° about (0, 0).
−1 0
3 −1
Find the image of Triangle A, by writing down the coordinates P’, Q’ and
21) If the
, is aDsingular
find
Triangle
A ismatrix
mapped+𝑥onto 2triangle
such thatmatrix,
RM(A) =
D. the value of x.
R’.
(a) Describe fully the single transformation that maps triangle A onto triangle B.
Draw and label triangle D.
[3]
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