Daily Practice · Higher Plus
July 1960 5-a-day
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The batch download puts all 5 tiers' July 1960 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1960
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1960Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 2nd July 1960y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 3rd July 1960A cuboid measures 13 cm by 5 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th July 1960A bag holds 3 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th July 1960A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 6th July 1960A rectangle is 16 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th July 1960Use the iteration x(n+1) = cube root of (6x(n) + 8) with x(0) = 4. Work out x(1) to 3 decimal places.
- 8th July 1960y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 36.
- 9th July 1960The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 10th July 1960A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 11th July 1960On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th July 1960Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 13th July 1960Work out the nth term of the quadratic sequence 3, 8, 17, 30, ...
- 14th July 1960A train slows steadily from 14 m/s to rest in 5 seconds. Work out its deceleration.
- 15th July 1960In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 16th July 1960The probability of winning a game is 3/4. A player expects 24 wins. How many games did they play?
- 17th July 1960A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 18th July 1960A block has mass 840 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th July 1960The point (-2, 6) lies on y = f(x). Write down its image on y = f(x) - 6.
- 20th July 1960y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 21st July 1960In a vector proof you find that vector PQ = 3a - 3b and vector RS = 15a - 15b. What does this show about PQ and RS?
- 22nd July 1960A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 23rd July 1960On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th July 1960x = 143 and y = 91, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th July 1960Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 26th July 1960y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 27th July 1960A cuboid measures 8 cm by 7 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th July 1960A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th July 1960A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 30th July 1960A car covers 580 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 31st July 1960f(x) = 3x - 4 and g(x) = 2x - 6. Work out fg(6).