Daily Practice · Higher Plus
July 1969 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1969 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1969
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1969Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 2nd July 1969Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 3rd July 1969y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 4th July 1969In a vector proof you find that vector PQ = a + 2b and vector RS = 3a + 6b. What does this show about PQ and RS?
- 5th July 1969A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 6th July 1969A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 7th July 1969A block has mass 270 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th July 1969f(x) = 6x - 6 and g(x) = 6x - 9. Work out fg(1).
- 9th July 1969y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 49.
- 10th July 1969A cuboid measures 10 cm by 6 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th July 1969A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th July 1969On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th July 1969x = 49 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th July 1969The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 15th July 1969A train slows steadily from 16 m/s to rest in 4 seconds. Work out its deceleration.
- 16th July 1969A cuboid measures 7 cm by 7 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th July 1969A bag holds 6 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th July 1969A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 19th July 1969A car covers 660 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 20th July 1969A quadratic sequence starts 6, 26, 56, 96. Work out the second difference, and the coefficient of n^2.
- 21st July 1969y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 22nd July 1969The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 23rd July 1969A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 24th July 1969On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th July 1969Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 26th July 1969Solve x^2 + 8x + 7 < 0.
- 27th July 1969y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 28th July 1969In 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.
- 29th July 1969The probability of winning a game is 4/5. A player expects 72 wins. How many games did they play?
- 30th July 1969A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 31st July 1969Simplify sqrt(8) + sqrt(2), giving your answer in the form a sqrt(b).