Daily Practice · Higher Plus
July 1954 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1954 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1954A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 2nd July 1954Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
- 3rd July 1954Write x^2 - 10x + 4 in the form (x + a)^2 + b.
- 4th July 1954y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 5th July 1954A cuboid measures 5 cm by 11 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th July 1954A bag holds 6 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th July 1954On 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?
- 8th July 1954Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
- 9th July 1954Work out the coordinates of the turning point of y = x^2 - 16x - 14.
- 10th July 1954y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 11th July 1954The 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.
- 12th July 1954A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 13th July 1954A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 14th July 1954A rectangle is 11 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th July 1954Simplify (x^2 + 4x + 3)/(x + 1).
- 16th July 1954y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 4.
- 17th July 1954In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 18th July 1954The probability of winning a game is 1/4. A player expects 30 wins. How many games did they play?
- 19th July 1954On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 20th July 1954Expand and simplify (8 + sqrt(11))(8 - sqrt(11)).
- 21st July 1954In an algebraic proof, how would you write an odd number in terms of an integer n?
- 22nd July 1954A train slows steadily from 40 m/s to rest in 5 seconds. Work out its deceleration.
- 23rd July 1954In a vector proof you find that vector PQ = 6a - 4b and vector RS = 24a - 16b. What does this show about PQ and RS?
- 24th July 1954A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 25th July 1954A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 26th July 1954A block has mass 670 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th July 1954Make x the subject of 3x + 5 = y(x + 5).
- 28th July 1954y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 29th July 1954A cuboid measures 11 cm by 10 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th July 1954A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st July 1954On 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?