Edexcel Jan 2020 IGCSE, 4MA1/2H questions (pdf)
- (a) Simplify x9/x2
(b) Write (78 x 74)/73 as a single power of 7
- Change 32.4 m3 into cm
- Show that 4 2/3 + 3 4/5 = 8 7/15
- The diagram shows a triangle.
Work out the value of x.
- Use ruler and compasses to construct the bisector of angle BAC.
You must show all your construction lines.
- A bag contains only red beads, blue beads, green beads and yellow beads.
The table gives the probabilities that, when a bead is taken at random from the bag, the bead will be blue or the bead will be yellow.
The probability that the bead will be green is twice the probability that the bead will be red.
Sofia takes at random a bead from the bag.
She writes down the colour of the bead and puts the bead back into the bag.
She does this 180 times.
Work out an estimate for the number of times she takes a red bead from the bag.
- (a) Solve the inequality 2x + 7 > 4
(b) Solve x2</2up> - 3x - 40 = 0
Show clear algebraic working.
- The table shows the cost, in euros, of Brigitte’s car insurance in each of the years 2016,
2017 and 2018
“The percentage increase in the cost of my car insurance from 2017 to 2018 is more than the percentage increase in the cost of my car insurance from 2016 to 2017”
(a) Is Brigitte correct?
You must show how you get your answer.
Henri wants to insure his car.
He gets a discount of 15% off the normal price.
Henri pays 952 euros for his car insurance after the discount.
(b) Work out the discount that Henri gets.
- The density of gold is 19.3 g/cm3 A gold bar has volume 150 cm3
Work out the mass of the gold bar.
- Change a speed of 50 metres per second to a speed in kilometres per hour.
- The diagram shows a shaded shape ABCD made from a semicircle ABC and a right-angled triangle ACD.
AC is the diameter of the semicircle ABC.
Work out the perimeter of the shaded shape.
Give your answer correct to 3 significant figures.
- Astrid wants to buy some oil.
She can buy the oil from either Dane Oil or Arctic Oil.
Here is information about the price that each company will charge Astrid.
Astrid wants to get the better value for money for the oil.
1 Dollar 6.57 Krone
From which company should she buy her oil, Dane Oil or Arctic Oil? You must show your working.
- A, B, C and D are points on a circle, centre O.
AOD is a diameter of the circle.
Angle CBD = 28°
Angle BDA = 32°
Find the size of angle BDC.
Give a reason for each stage of your working.
- There are 20 glasses in a cupboard.
13 of the glasses are large
7 of the glasses are small
Roberto takes at random two glasses from the cupboard.
(a) Complete the probability tree diagram.
(b) Work out the probability that Roberto takes two small glasses.
- Here are six graphs.
Complete the table below with the letter of the graph that could represent each given equation.
Write your answers on the dotted lines.
- Make x the subject of y =
- Prove that the difference between two consecutive square numbers is always an odd number. Show clear algebraic working.
- The histogram gives information about the times, in minutes, that some customers spent in a supermarket.
(a) Work out an estimate for the proportion of these customers who spent between 17 minutes and 35 minutes in the supermarket.
One of the customers is selected at random.
Given that this customer had spent more than 30 minutes in the supermarket,
(b) find the probability that this customer spent more than 36 minutes in the supermarket.
- (a) Write down an equation of a line that is parallel to the line with equation y = 7 — 4x
The line L passes through the points with coordinates (—3, 1) and (2, —2)
(b) Find an equation of the line that is perpendicular to L and passes through the point with coordinates (—6, 4)
Give your answer in the form ax + by + c 0 where a, b and c are integers.
- The area of a rectangle is 18cm2
The length of the rectangle is (&rdaic;7 + 1) cm.
Without using a calculator and showing each stage of your working,
find the width of the rectangle.
Give your answer in the form a√b + c where a, b and c are integers.
- The diagram shows a sketch of part of the curve with equation y = f(x)
There is one maximum point on this curve.
The coordinates of this maximum point are (4, 6)
(a) Write down the coordinates of the maximum point on the curve with equation
(i) y = f(x + 4)
(ii) y = f(2x)
The equation of a curve C is y = x2 + 3x + 4
The curve C is transformed to curve S under the translation (4,6)
(b) Find an equation of curve S.
- The line with equation y = x + 2 intersects the curve with equation x2 + y 2 — 2y = 24 at the points A and B.
Find the coordinates of A and B. Show clear algebraic working.
- ABC is a triangle.
The midpoint of BC is M.
P is a point on AM.
Find the ratio AP:PM
- Express as a single fraction in its simplest form.
- Mario is going to save $50 in the year 2021
He is going to continue to save, up to and including the year 2070, by increasing the amount he saves each year by $k
Mario will save a total of $33 125 from 2021 to 2070
Work out the value of k.
- Here is a sector, AOB, of a circle with centre O and angle AOB = x°
The sector can form the curved surface of a cone by joining OA to OB.
The height of the cone is 25 cm. The volume of the cone is 1600 cm3
Work out the value of x.
Give your answer correct to the nearest whole number.
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