Daily Practice · Higher Plus
July 1972 5-a-day
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The batch download puts all 5 tiers' July 1972 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1972A bag holds 3 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd July 1972A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 3rd July 1972A block has mass 600 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th July 1972Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 5th July 1972y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 6th July 1972The 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.
- 7th July 1972A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 8th July 1972On 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?
- 9th July 1972x = 125 and y = 36, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th July 1972Use the iteration x(n+1) = cube root of (11x(n) + 9) with x(0) = 2. Work out x(1) to 3 decimal places.
- 11th July 1972y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 12th July 1972In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 13th July 1972The probability of winning a game is 1/5. A player expects 7 wins. How many games did they play?
- 14th July 1972A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 15th July 1972A car covers 740 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.
- 16th July 1972Work out the nth term of the quadratic sequence 5, 14, 29, 50, ...
- 17th July 1972y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 64.
- 18th July 1972In a vector proof you find that vector PQ = 5a + b and vector RS = 15a + 3b. What does this show about PQ and RS?
- 19th July 1972A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 20th July 1972On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st July 1972Rationalise the denominator of 77/sqrt(7), giving your answer in its simplest form.
- 22nd July 1972The point (5, 5) lies on y = f(x). Write down its image on y = f(x - 4).
- 23rd July 1972A train slows steadily from 14 m/s to rest in 10 seconds. Work out its deceleration.
- 24th July 1972A cuboid measures 8 cm by 11 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th July 1972A 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?
- 26th July 1972A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 27th July 1972Simplify sqrt(80) + sqrt(80), giving your answer in the form a sqrt(b).
- 28th July 1972Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 29th July 1972y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 30th July 1972A cuboid measures 4 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st July 1972A bag holds 5 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?