Daily Practice · Higher Plus
July 1979 5-a-day
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The batch download puts all 5 tiers' July 1979 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1979
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1979A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 2nd July 1979A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 3rd July 1979Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
- 4th July 1979Use the iteration x(n+1) = cube root of (6x(n) + 9) with x(0) = 4. Work out x(1) to 3 decimal places.
- 5th July 1979y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 49.
- 6th July 1979In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 7th July 1979The probability of winning a game is 1/5. A player expects 30 wins. How many games did they play?
- 8th July 1979On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 9th July 1979A block has mass 630 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th July 1979Work out the nth term of the quadratic sequence 6, 23, 48, 81, ...
- 11th July 1979A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 12th July 1979In a vector proof you find that vector PQ = 4a - 4b and vector RS = 20a - 20b. What does this show about PQ and RS?
- 13th July 1979A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 14th July 1979A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 15th July 1979x = 59 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th July 1979The point (-1, 1) lies on y = f(x). Write down its image on y = f(-x).
- 17th July 1979y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 18th July 1979A cuboid measures 15 cm by 5 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th July 1979A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th July 1979On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st July 1979A car covers 660 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.
- 22nd July 1979Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 23rd July 1979y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 24th July 1979A cuboid measures 14 cm by 13 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th July 1979A bag holds 5 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th July 1979A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 27th July 1979Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 28th July 1979f(x) = 5x + 2 and g(x) = 6x - 8. Work out fg(-3).
- 29th July 1979y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 16.
- 30th July 1979The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 31st July 1979A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/9. Work out r.