Daily Practice · Higher Plus
July 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1965 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1965A cuboid measures 5 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd July 1965A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd July 1965A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 4th July 1965x = 195 and y = 80, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th July 1965f(x) = 2x + 9. Work out the inverse function f^-1(x).
- 6th July 1965y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 64.
- 7th July 1965A cuboid measures 7 cm by 10 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th July 1965A bag holds 4 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th July 1965On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th July 1965A car covers 490 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.
- 11th July 1965Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 12th July 1965A train slows steadily from 26 m/s to rest in 4 seconds. Work out its deceleration.
- 13th July 1965The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 14th July 1965A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 15th July 1965A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 16th July 1965Rationalise the denominator of 45/sqrt(5), giving your answer in its simplest form.
- 17th July 1965Use the iteration x(n+1) = cube root of (6x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
- 18th July 1965y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 19th July 1965In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 20th July 1965The probability of winning a game is 9/10. A player expects 36 wins. How many games did they play?
- 21st July 1965On 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?
- 22nd July 1965Simplify sqrt(12) + sqrt(48), giving your answer in the form a sqrt(b).
- 23rd July 1965Work out the nth term of the quadratic sequence 4, 15, 34, 61, ...
- 24th July 1965y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 25th July 1965In a vector proof you find that vector PQ = 4a - 2b and vector RS = 20a - 10b. What does this show about PQ and RS?
- 26th July 1965A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 27th July 1965A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 28th July 1965A rectangle is 28 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th July 1965The point (4, 0) lies on y = f(x). Write down its image on y = f(-x).
- 30th July 1965y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 81.
- 31st July 1965A cuboid measures 15 cm by 7 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.