Daily Practice · Higher Plus
June 1983 5-a-day
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The batch download puts all 5 tiers' June 1983 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1983Use the iteration x(n+1) = cube root of (9x(n) + 5) with x(0) = 5. Work out x(1) to 3 decimal places.
- 2nd June 1983y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 3rd June 1983A cuboid measures 12 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th June 1983A bag holds 3 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th June 1983On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th June 1983A block has mass 830 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th June 1983Work out the nth term of the quadratic sequence 4, 13, 30, 55, ...
- 8th June 1983y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 9th June 1983The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 10th June 1983A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 11th June 1983A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 12th June 1983x = 67 and y = 29, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th June 1983The point (-2, -3) lies on y = f(x). Write down its image on y = -f(x).
- 14th June 1983y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 81.
- 15th June 1983In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 16th June 1983The probability of winning a game is 2/5. A player expects 8 wins. How many games did they play?
- 17th June 1983On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th June 1983A car covers 790 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th June 1983Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 20th June 1983A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 21st June 1983In a vector proof you find that vector PQ = 6a - 2b and vector RS = 30a - 10b. What does this show about PQ and RS?
- 22nd June 1983A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 23rd June 1983A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 24th June 1983Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 25th June 1983f(x) = 4x + 3 and g(x) = 2x + 3. Work out fg(1).
- 26th June 1983y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 27th June 1983A cuboid measures 4 cm by 10 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th June 1983A bag holds 5 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th June 1983On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th June 1983Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).