Daily Practice · Higher Plus
July 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1959 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1959A quadratic sequence starts 4, 21, 46, 79. Work out the second difference, and the coefficient of n^2.
- 2nd July 1959y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 3rd July 1959A cuboid measures 9 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th July 1959A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th July 1959On 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?
- 6th July 1959A block has mass 590 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.
- 7th July 1959Solve x^2 + 9x + 18 > 0.
- 8th July 1959y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 9th July 1959A cuboid measures 11 cm by 7 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th July 1959A bag holds 6 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th July 1959A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 12th July 1959x = 43 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th July 1959Write x^2 + 2x + 1 in the form (x + a)^2 + b.
- 14th July 1959y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 49.
- 15th July 1959The 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.
- 16th July 1959A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 17th July 1959On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th July 1959A car covers 260 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.
- 19th July 1959Work out the coordinates of the turning point of y = x^2 + 12x - 4.
- 20th July 1959A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 21st July 1959In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 22nd July 1959The probability of winning a game is 1/4. A player expects 18 wins. How many games did they play?
- 23rd July 1959A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 24th July 1959Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.
- 25th July 1959Simplify (x^2 + 2x - 15)/(x + 5).
- 26th July 1959y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 27th July 1959In a vector proof you find that vector PQ = 6a - 3b and vector RS = 24a - 12b. What does this show about PQ and RS?
- 28th July 1959A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 29th July 1959On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th July 1959Simplify sqrt(80) + sqrt(20), giving your answer in the form a sqrt(b).
- 31st July 1959In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?