Daily Practice · Higher Plus
July 1966 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1966 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1966
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1966y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 36.
- 2nd July 1966A cuboid measures 7 cm by 4 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd July 1966A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th July 1966On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th July 1966Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
- 6th July 1966Write x^2 + 10x - 4 in the form (x + a)^2 + b.
- 7th July 1966A train slows steadily from 15 m/s to rest in 10 seconds. Work out its deceleration.
- 8th July 1966The 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.
- 9th July 1966A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 10th July 1966A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 11th July 1966A block has mass 590 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th July 1966Work out the coordinates of the turning point of y = x^2 - 4x - 13.
- 13th July 1966y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 14th July 1966In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 15th July 1966The probability of winning a game is 3/4. A player expects 42 wins. How many games did they play?
- 16th July 1966On 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?
- 17th July 1966x = 152 and y = 94, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th July 1966Simplify (x^2 + x - 12)/(x + 4).
- 19th July 1966y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 20th July 1966In a vector proof you find that vector PQ = 4a - 3b and vector RS = 8a - 6b. What does this show about PQ and RS?
- 21st July 1966A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 22nd July 1966A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 23rd July 1966A car covers 550 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.
- 24th July 1966In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 25th July 1966y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 81.
- 26th July 1966A cuboid measures 9 cm by 13 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th July 1966A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th July 1966On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th July 1966Rationalise the denominator of 44/sqrt(11), giving your answer in its simplest form.
- 30th July 1966Make x the subject of 7x + 5 = y(x + 5).
- 31st July 1966A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.