Daily Practice · Higher Plus
June 1984 5-a-day
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The batch download puts all 5 tiers' June 1984 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1984
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1984Simplify (x^2 - 4x - 5)/(x + 1).
- 2nd June 1984y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 3rd June 1984The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 4th June 1984A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 5th June 1984A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 6th June 1984A rectangle is 12 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th June 1984In an algebraic proof, how would you write an even number in terms of an integer n?
- 8th June 1984y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 64.
- 9th June 1984In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 10th June 1984The probability of winning a game is 1/8. A player expects 12 wins. How many games did they play?
- 11th June 1984On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th June 1984Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 13th June 1984Make x the subject of 3x + 6 = y(x + 6).
- 14th June 1984A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
- 15th June 1984In a vector proof you find that vector PQ = 4a + 2b and vector RS = 8a + 4b. What does this show about PQ and RS?
- 16th June 1984A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 17th June 1984A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 18th June 1984A block has mass 680 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th June 1984Write 3/(x - 6) + 4/(x + 6) as a single fraction.
- 20th June 1984y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 21st June 1984A cuboid measures 8 cm by 11 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd June 1984A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd June 1984On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th June 1984x = 97 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th June 1984Solve 2x^2 - 15x + 25 = 0.
- 26th June 1984y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 27th June 1984A cuboid measures 10 cm by 9 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th June 1984A bag holds 4 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th June 1984A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 30th June 1984A car covers 810 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.