Daily Practice · Higher Plus
July 1958 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1958 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1958
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1958A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
- 2nd July 1958In a vector proof you find that vector PQ = a + 3b and vector RS = 4a + 12b. What does this show about PQ and RS?
- 3rd July 1958A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 4th July 1958A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 5th July 1958A car covers 150 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th July 1958Solve 20x^2 - 29x + 6 = 0.
- 7th July 1958y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 8th July 1958A cuboid measures 15 cm by 14 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th July 1958A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th July 1958On 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?
- 11th July 1958Rationalise the denominator of 44/sqrt(11), giving your answer in its simplest form.
- 12th July 1958f(x) = 6x + 8. Work out the inverse function f^-1(x).
- 13th July 1958y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 14th July 1958A cuboid measures 6 cm by 14 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th July 1958A bag holds 7 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th July 1958A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 17th July 1958Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).
- 18th July 1958Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 19th July 1958y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 81.
- 20th July 1958The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 21st July 1958A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 22nd July 1958On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd July 1958A rectangle is 25 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th July 1958Use the iteration x(n+1) = cube root of (6x(n) + 3) with x(0) = 5. Work out x(1) to 3 decimal places.
- 25th July 1958A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 26th July 1958In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 27th July 1958The probability of winning a game is 1/5. A player expects 4 wins. How many games did they play?
- 28th July 1958A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 29th July 1958Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
- 30th July 1958Work out the nth term of the quadratic sequence 9, 17, 27, 39, ...
- 31st July 1958y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.