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IGCSE Maths 4MA1 Year 10 starter questions: weeks 23–33

40 short questions to open a lesson for Edexcel IGCSE Maths A (4MA1) Higher, Year 10, weeks 23–33 of the teaching year, three or four a week. Each question is shown as an image with its text underneath; the answers and mark schemes are free on the free weekly starters page, to show or project in class.

Week 23

Question 1: Quadratic Equations
Solve x² + 2x - 24 = 0.
Question 2: Quadratic Equations
Solve 3x² - 10x = 8.
Question 3: Completing the Square
Write x² - 8x + 3 in the form (x + p)² + q.
Question 4: Forming Quadratics
A rectangle has length (x + 5) cm and width x cm. Its area is 84 cm². Work out the value of x.

Week 24

Question 1: Quadratic Graphs
Write down the equation of the line of symmetry of y = x² - 6x + 5 and the coordinates of its turning point.
Question 2: Quadratic Graphs
Complete: for y = x² - 2x - 3, when x = -2, y = … and the graph crosses the x-axis at x = …
Question 3: Growth by Multipliers
The number of bacteria is modelled by N = 200 × 3^t, where t is time in hours. Work out N when t = 4.
Question 4: Distance–Time Graphs
On a distance–time graph, a cyclist travels from (0, 0) to (40, 12), where time is in minutes and distance is in km. Work out the speed in km/h.

Week 25

Question 1: Compound Interest
£2500 is invested at r% compound interest per year. After 2 years it is worth £2704. Find r.
Question 2: Indices
Solve 2^x = 1/32.
Question 3: Quadratics
Solve (x + 3)² = 2x + 14.
Question 4: Inequalities
Solve -3 < 2x + 5 ≤ 11.

Week 26

Question 1: Types of Data
State whether each is discrete or continuous: (a) the number of goals scored in a match, (b) the time taken to run 400 m.
Question 2: Averages
Find the median and range of: 12, 7, 19, 4, 15, 9, 11, 20.
Question 3: Mean
The mean of five numbers is 14. Four of the numbers are 9, 17, 12 and 20. Find the fifth number.
Question 4: Pie Charts
In a survey of 72 students, 22 chose football. Work out the angle for football on a pie chart.

Week 27

Question 1: Mean from a Frequency Table
The table shows the number of pets owned by 20 students: 0 pets: 5; 1 pet: 8; 2 pets: 4; 3 pets: 3. Work out the mean number of pets.
Question 2: Estimated Mean
Times (t s): 0 < t ≤ 10: 4; 10 < t ≤ 20: 9; 20 < t ≤ 40: 7. Work out an estimate for the mean time.
Question 3: Median Class
For the grouped data above, write down the class containing the median.
Question 4: Frequency Polygons
When drawing a frequency polygon for grouped data, at what x-value is the point for the class 20 < t ≤ 40 plotted?

Week 28

Question 1: Histograms
A class 10 < h ≤ 25 has frequency 36. Work out the frequency density.
Question 2: Histograms
On a histogram, the bar for 40 < m ≤ 45 has frequency density 6.8. Work out the frequency.
Question 3: Quartiles
Find the interquartile range of: 3, 5, 6, 8, 9, 12, 14, 15, 18, 21, 25.
Question 4: Cumulative Frequency
Frequencies for consecutive classes are 6, 14, 22, 11, 7. Write down the cumulative frequencies.

Week 29

Question 1: Cumulative Frequency
A cumulative frequency graph shows 80 values. Which cumulative frequencies would you read across from to estimate the median, the lower quartile and the upper quartile?
Question 2: Comparing Distributions
Group A: median 34, IQR 12. Group B: median 41, IQR 6. Make two comparisons.
Question 3: Estimated Mean
20 boys have mean height 162 cm and 30 girls have mean height 157 cm. Work out the mean height of all 50 students.
Question 4: Histograms
A histogram bar for 0 < t ≤ 20 has height 1.5. The bar for 20 < t ≤ 30 has height 4.2. How many values are there in total in these two classes?

Week 30

Question 1: Sample Spaces
Two fair dice are rolled and the scores are added. Work out the probability that the total is 8.
Question 2: Speed
A car travels 45 km at 60 km/h and then 30 km at 40 km/h. Work out its average speed for the whole journey.
Question 3: Simultaneous Equations
Solve 4x - 3y = 18 and 2x + 5y = -4.
Question 4: Sectors
A sector of a circle of radius 6 cm has area 15π cm². Work out the angle of the sector.

Week 32

Question 1: Factorising
Factorise fully 4x² - 100.
Question 2: Changing the Subject
Make x the subject of y = √((x - 3)/2).
Question 3: Midpoints
Find the midpoint of P(-3, 8) and Q(7, -2).
Question 4: Gradient
Line L passes through (0, -4) and (3, 5). Write down the equation of L.

Week 33

Question 1: Trigonometry
A 5 m ramp rises 0.6 m vertically. Work out the angle the ramp makes with the horizontal, to 1 decimal place.
Question 2: Sequences
The first term of a sequence is 3 and the term-to-term rule is 'multiply by 2 then subtract 1'. Write down the next three terms.
Question 3: Pythagoras
Work out the length of the diagonal of a square with side 7 cm. Give your answer as a surd in simplest form.
Question 4: Percentages
Express £18 as a percentage of £48.

More starter questions

Other weeks: Weeks 1–11 · Weeks 12–22 · Weeks 23–33. Answers and mark schemes, free for everyone, are on the free weekly starters page.

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