Daily Practice · Higher Plus
July 1987 5-a-day
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The batch download puts all 5 tiers' July 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1987A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 2nd July 1987On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd July 1987Rationalise the denominator of 8/sqrt(2), giving your answer in its simplest form.
- 4th July 1987In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 5th July 1987y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 6th July 1987A cuboid measures 8 cm by 4 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th July 1987A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th July 1987A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 9th July 1987Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
- 10th July 1987Make x the subject of 3x + 6 = y(x + 6).
- 11th July 1987y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 25.
- 12th July 1987A cuboid measures 12 cm by 10 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th July 1987A bag holds 4 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th July 1987On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th July 1987A rectangle is 11 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th July 1987Write 5/(x - 1) + 3/(x + 1) as a single fraction.
- 17th July 1987A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
- 18th July 1987The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 19th July 1987A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 20th July 1987A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 21st July 1987Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 22nd July 1987Solve 10x^2 + x - 3 = 0.
- 23rd July 1987y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 24th July 1987In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 25th July 1987The probability of winning a game is 2/5. A player expects 26 wins. How many games did they play?
- 26th July 1987On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th July 1987A block has mass 270 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th July 1987f(x) = 3x + 8. Work out the inverse function f^-1(x).
- 29th July 1987y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 30th July 1987In a vector proof you find that vector PQ = 4a - 6b and vector RS = 20a - 30b. What does this show about PQ and RS?
- 31st July 1987A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.