Daily Practice · Higher Plus
July 1955 5-a-day
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The batch download puts all 5 tiers' July 1955 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1955A bag holds 5 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd July 1955On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 3rd July 1955x = 82 and y = 68, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th July 1955Work out the nth term of the quadratic sequence 6, 15, 30, 51, ...
- 5th July 1955y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 6th July 1955The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 7th July 1955A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 8th July 1955A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 9th July 1955A car covers 150 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th July 1955The point (-2, -6) lies on y = f(x). Write down its image on y = f(-x).
- 11th July 1955y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 16.
- 12th July 1955In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 13th July 1955The probability of winning a game is 3/5. A player expects 54 wins. How many games did they play?
- 14th July 1955On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th July 1955Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 16th July 1955Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 17th July 1955A train slows steadily from 12 m/s to rest in 8 seconds. Work out its deceleration.
- 18th July 1955In a vector proof you find that vector PQ = 4a + 6b and vector RS = 16a + 24b. What does this show about PQ and RS?
- 19th July 1955A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 20th July 1955A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 21st July 1955Simplify sqrt(20) + sqrt(45), giving your answer in the form a sqrt(b).
- 22nd July 1955f(x) = 3x - 8 and g(x) = 5x + 2. Work out fg(4).
- 23rd July 1955y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 24th July 1955A cuboid measures 7 cm by 12 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th July 1955A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th July 1955On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th July 1955A rectangle is 13 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th July 1955The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 29th July 1955y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 30th July 1955A cuboid measures 9 cm by 13 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st July 1955A bag holds 5 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?