4MA1 Mathematics A: May/June 2019 Paper 1HHigher Tier Paper 1

Show that 4 23÷ 1 19= 4 15[3]

Jalina left her home at 10 00 to cycle to a park. On her way to the park, she stopped at a friend’s house and then continued her journey to the park. Here is the distance-time graph for her journey to the park.

(a)On her journey to the park, did Jalina cycle at a faster speed before or after she stopped at her friend’s house? Give a reason for your answer.

[1]

Jalina stayed at the park for 45 minutes. She then cycled, without stopping, at a constant speed of 16 km/h from the park back to her home.

(b)Show all this information on the distance-time graph.[2]

(c)Work out Jalina’s average cycling speed, in kilometres per hour, for the complete journey to the park and back. Do not include the times when she was not cycling in your calculation. Give your answer correct to 1 decimal place.

_km/h[3]

(a)Simplify e⁹÷ e⁵

[1]

[1]

(c)Expand and simplify (x + 9)(x – 2)

[2]

(d)Factorise fully 16c⁴ p²+ 20cp³

[2]

(a)Complete the table of values for y = x²íxí

[2]

(b)On the grid, draw the graph of y = x²íx x

[2]

Becky has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

Becky is going to throw the dice 200 times.

Work out an estimate for the number of times that the dice will land on an even number.

[4]

The diagram shows a solid cuboid made from wood.

The wood has density 0.7 g/cm³

Work out the mass of the cuboid.

_grams[3]

(a)Write 5.7 × 10⁶ as an ordinary number.

[1]

(b)Write 0.004 in standard form.

[1]

(c)Work out 2 × 106.4 × 10₋₂

[2]

On 1st January 2016 Li bought a boat for $170 000 The value of the boat depreciates by 8% per year.

Work out the value of the boat on 1st January 2019 Give your answer correct to the nearest dollar.

$ [3]

The diagram shows a shape made from a right-angled triangle and a semicircle.

AC is the diameter of the semicircle. BA = BC = 6 cm Angle ABC = 90°

Work out the area of the shape. Give your answer correct to 1 decimal place.

_cm²[5]

A = 2ⁿ × 3 × 5^m

Write 8A as a product of powers of its prime factors.

[2]

C = bía

a = 6 correct to the nearest integer b = 15 correct to the nearest 5

Work out the upper bound for the value of C Show your working clearly.

[3]

(a)Factorise 2x²íx + 6

[2]

(b)Solve 4m + 93 m

Show clear algebraic working.

m = [4]

(c)Write yy in the form y^b where b is a fraction.

[2]

In group C, there are 6 girls and 8 boys. In group D, there are 3 girls and 7 boys.

A team is made by picking at random one child from group C and one child from group D.

(a)Complete the probability tree diagram.

[2]

(b)Work out the probability that there are two boys in the team.

[2]

After the first team has been picked, a second team is picked. One child is picked at random from the children left in group C and one child is picked at random from the children left in group D.

(c)Work out the probability that there are two boys in each of the two teams.

[3]

E = {positive integers less than 20} A = {x : x  12} B = {x : 7 - x  16}

(a)List the members of A ∩ B

[2]

C is a set such that C ⊂ A and n(C௘  

Given that all members of C are even numbers,

(b)list the members of one possible set C.

[1]

Use algebra to show that the recurring decimal 0.254 = 1455[2]

Here are the first five terms of an arithmetic sequence.

Find the sum of the first 100 terms of this sequence.

[2]

A and B are two similar vases.

Vase A has height 24 cm. Vase B has height 36 cm.

Vase A has a surface area of 960 cm²

(a)Work out the surface area of vase B.

_cm²[2]

Vase B has a volume of V cm³

(b)Find in terms of V, an expression for the volume, in cm³, of vase A.

_cm³[2]

The diagram shows triangle PQR.

Calculate the length of PR. Give your answer correct to 3 significant figures.

_cm[3]

The table gives information about the heights of some trees.

On the grid, draw a histogram for this information.

[3]

B

A, B, C and D are points on a circle. TDV is the tangent to the circle at D.

AB = AD Angle ADT = 71°

Work out the size of angle BCD. Give a reason for each stage of your working.

[5]

A solid is made from a hemisphere and a cylinder. The plane face of the hemisphere coincides with the upper plane face of the cylinder.

The hemisphere and the cylinder have the same radius.

The ratio of the radius of the cylinder to the height of the cylinder is 1 : 3

Given that the solid has volume 792ʌ cm³ work out the height of the solid.

_cm[5]

The graph of y = sinx° for 0 - x - 360 is drawn on the grid.

(a)On the grid, draw the graph of y = 2sin(x + 30)° for 0 - x - 360[2]

(b)(i)Write x²íx + 10 in the form (xía)²+ b where a and b are integers.

[2]

(ii)Hence, describe fully the single transformation that maps the curve with equation y = x² onto the curve with equation y = x²íx + 10

[2]

ABCD is a kite with AB = AD and CB = CD.

B is the point with coordinates (10, 19) D is the point with coordinates (2, 7)

Find an equation of the line AC. Give your answer in the form py + qx = U where p, q and U are integers.

[5]

A particle P is moving along a straight line that passes through the fixed point O. The displacement, s metres, of P from O at time t seconds is given by

Find the value of t for which the acceleration of P is 3 m/s²

t = [4]