GCSE MATHEMATICS Higher Tier, NON-CALCULATOR REVISION ...

GCSE MATHEMATICS Higher Tier, NON-CALCULATOR
REVISION SHEET
1. In the diagram, AOB is a diameter of the circle, centre O.
TS is a tangent to the circle at C.
Angle ABC = 57°
T
C
Not drawn
accurately
S
Calculate
A
O
57º
B
(a)
(b)
Angle CAB
Angle ACS.
2. y is inversely proportional to x 2 .
When x = 2, y = 5
(a) Find the value of y when x = 4
(b) Find the values of x when y = 0.2
3. A bag contains two black discs and three white discs.
Three children play a game in which each draws a disc from the bag.
Parveen goes first, then Seema, and Jane is last.
Each time a disc is withdrawn it is not replaced.
The first child to draw a white disc wins the game.
(a)
In a game, calculate the probability that
(i) Parveen wins,
(ii) Seema wins.
They replace the discs and play the game a second time.
(b)
Calculate the probability that
(i) Parveen wins neither the first nor the second game.
(ii) Jane wins both games.
4. Make x the subject of the formula y =
4x
x + 2
5. Factorise
(a) 2x 2 – 7x – 15
(b) x 2 – 25y 2
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6. You are given that
cos 48° = 0.669
Find another angle between 0° and 360° that also has a cosine of 0.669.
{Hint, you will need to sketch the graph of y = cos x.}
7. (a) (i) Show that 12 = 2 3
(ii)
Expand and simplify
( 2 +
6) 2
(b)
B
Not drawn accurately
(2 + 3)
1
A
( 2 + 6)
C
Is triangle ABC right-angled?
Show your working clearly.
8. A magic square is shown below.
Every row, column and diagonal adds up to the same total.
In this example the total is 3.
4 –1 0
–3 1 5
2 3 –2
(a)
(b)
Paul says, “If I multiply every number in the magic square by –6, the new total will
be –18.” Show clearly that this is true for the first column of numbers.
Here is a different magic square.
Every row, column and diagonal adds up to the same total.
2x 1 –2y
3 y + 8 3x – 5
x 9 2y + 8
(i)
(ii)
By considering the first two rows show that
x + 3y + 5 = 0
By considering other rows, columns or diagonals, find the values of x and y
and hence complete the magic square.
3
1
9
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{Hint: simultaneous equations.}

Answers.
1. (a) 33 o (b) 123 o .
20
2. {y =
x } 2
(a) y = 5 4
(b) x = 10 or 10.
3. (a) (i)
(b)
(i)
3
5
2
5 × 2 5 = 4
25
(ii)
(ii)
2
5 × 3 4 = 3
10 .
1 1 1
× = .
10 10 100
4. y(x + 2) = 4x
yx + 2y = 4x
2y = 4x yx
2y = (4 y)x
2y
= x.
4 y
5. (a) (2x + 3)(x 5).
(b) (x 5y)(x + 5y).
6. 312 o .
7. (a) (ii) 8 + 2 12 which equals 8 + 4 3 .
(b) Check Pythagoras: 1 2 + ( 2 + 3) 2
= 1 + 4 + 4 3 + 3 = 8 + 4 3 .
( 2 + 6 ) 2
= 8 + 4 3 from (a) (ii).
This confirms that the triangle is right angled.
8. (a) (6) × 4 + (6) × (3) + (6) × 2 = 24 + 18 12 = 18.
(b) (ii) x = 4, y = 3.
8 1 6
3 5 7
4 9 2
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