Daily Practice · Higher Plus
July 1964 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1964 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1964
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1964A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 2nd July 1964On 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?
- 3rd July 1964Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 4th July 1964The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 5th July 1964y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 6th July 1964A cuboid measures 14 cm by 14 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th July 1964A 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?
- 8th July 1964A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 9th July 1964Simplify sqrt(18) + sqrt(18), giving your answer in the form a sqrt(b).
- 10th July 1964A quadratic sequence starts 8, 19, 38, 65. Work out the second difference, and the coefficient of n^2.
- 11th July 1964y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 36.
- 12th July 1964A cuboid measures 7 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th July 1964A bag holds 5 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th July 1964On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th July 1964A rectangle is 23 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th July 1964Solve x^2 + 11x + 24 < 0.
- 17th July 1964A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 18th July 1964The 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.
- 19th July 1964A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
- 20th July 1964A 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?
- 21st July 1964Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 22nd July 1964Write x^2 - 8x - 14 in the form (x + a)^2 + b.
- 23rd July 1964y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 24th July 1964In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 25th July 1964The probability of winning a game is 5/8. A player expects 30 wins. How many games did they play?
- 26th July 1964On 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?
- 27th July 1964A block has mass 700 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th July 1964Work out the coordinates of the turning point of y = x^2 - 12x + 7.
- 29th July 1964y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 30th July 1964In a vector proof you find that vector PQ = 6a + 4b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 31st July 1964A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.