## SAT Test 1 Explanations

click to enlarge each explanation

### Test 1 Section 3

You may not use a calculator.

Question 1

If (x-1) / 3 = k and k = 3, what is the value of x ?

Question 2

For i = √-1, what is the sum (7 + 3i) + (-8 + 9i) ?

Question 3

On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which if the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?

Question 4

Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 - 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?

Question 5

Which of the following is equivalent to the expression above?

Question 6

A pediatrician uses the model above to estimate the height h of a boy, in inches, in terms of the boy's age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy's height each year?

Question 7

The formula above gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months. Which of the following gives P in terms of m, r, and N ?

Question 8

If a/b = 2, what is the value of 4b/a ?

Question 9

What is the solution (x, y) to the system of equations above?

Question 10

For the function g defined above, a is a constant and g(4) = 8. What is the value of g(-4) ?

Question 11

In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?

Question 12

A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line?

Question 13

If x > 3, which of the following is equivalent to

Question 14

If 3x - y = 12, what is the value of 8^x / 2^y ?

Question 15

If (ax + 2)(bx + 7) = 15x² + cx + 14 for all values of x, and a + b = 8, what are the two possible values for c ?

Question 16

If t > 0 and t² - 4 = 0, what is the value of t ?

Question 17

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD, and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and ∠AEB and ∠CDB have the same measure. What is the value of x ?

Question 18

According to the system of equations above, what is the value of x ?

Question 19

In a right triangle, one angle measures x°, where sin x° = 4/5. What is cos(90° - x°) ?

Question 20

If a = 5√2 and 2a = √2x, what is the value of x ?

{"items":["498779c9-d014-488d-b873-7c9479d7f1dc","113ecf75-6148-472a-9944-4143f3ad88c2","91cc693a-0229-4ada-b4fa-98c7911a2989","3a4067b8-9bbb-45b8-bd76-a3cb53752910","f80d9a34-cb09-485c-aed9-2c65ed7b3827","198b3fb3-18c5-486b-9674-d864d7d1c0f0","1cb494df-770f-4ecb-b7d9-98fe2ef799a8","c40393a5-61bb-4c54-8a85-46a72fb65105","5093289c-2d00-4a6c-97d4-1314b7dd50fc","e3c65449-5c11-4d94-b7ac-9cbc7f18f536","7123b7a6-577a-4695-8314-83a8ad6c00ca","8f34accb-6363-489f-8f64-e0395e4ce4d3","e59b1e34-a18b-488a-970c-df656c8999ef","b13327a3-de46-4a5d-9895-75a5c8b3482c","ca6dfcc6-7103-447e-a301-3a3871184007","63235f2a-a6b9-4dd6-9bb9-c05e189edf75","faf1b04d-0ee0-49a6-8b1d-ce72f83fbebd","7a5e9c69-de3c-4b78-9b80-44cf8268e86e","1d855460-c7cb-4942-a8ba-99147fd0d25a","ee487191-8869-4519-9d12-798e017ae808"],"styles":{"galleryType":"Columns","groupSize":1,"showArrows":true,"cubeImages":true,"cubeType":"fill","cubeRatio":0.75,"isVertical":true,"gallerySize":320,"collageAmount":0,"collageDensity":0,"groupTypes":"1","oneRow":false,"imageMargin":7.5,"galleryMargin":0,"floatingImages":0,"chooseBestGroup":true,"smartCrop":false,"hasThumbnails":false,"enableScroll":true,"isGrid":true,"isSlider":false,"isColumns":false,"isSlideshow":false,"cropOnlyFill":false,"fixedColumns":5,"enableInfiniteScroll":true,"isRTL":false,"minItemSize":50,"rotatingGroupTypes":"","rotatingCubeRatio":"","gallerySliderImageRatio":1.7777777777777777,"numberOfImagesPerRow":5,"numberOfImagesPerCol":1,"groupsPerStrip":0,"borderRadius":0,"boxShadow":0,"gridStyle":1,"mobilePanorama":false,"placeGroupsLtr":false,"viewMode":"preview","thumbnailSpacings":9,"galleryThumbnailsAlignment":"left","isMasonry":false,"isAutoSlideshow":false,"slideshowLoop":false,"autoSlideshowInterval":4,"bottomInfoHeight":0,"titlePlacement":"SHOW_ABOVE","galleryTextAlign":"center","scrollSnap":false,"itemClick":"expand","fullscreen":true,"videoPlay":"hover","scrollAnimation":"SLIDE_UP","scrollDirection":0,"overlayAnimation":"EXPAND","arrowsPosition":0,"arrowsSize":23,"watermarkOpacity":40,"watermarkSize":40,"useWatermark":true,"watermarkDock":{"top":"auto","left":"auto","right":0,"bottom":0,"transform":"translate3d(0,0,0)"},"loadMoreAmount":"all","defaultShowInfoExpand":1,"allowLinkExpand":true,"expandInfoPosition":0,"allowFullscreenExpand":true,"fullscreenLoop":false,"galleryAlignExpand":"left","addToCartBorderWidth":1,"addToCartButtonText":"","slideshowInfoSize":200,"playButtonForAutoSlideShow":false,"allowSlideshowCounter":false,"hoveringBehaviour":"APPEARS","thumbnailSize":120,"magicLayoutSeed":1,"imageHoverAnimation":"ZOOM_IN","imagePlacementAnimation":"NO_EFFECT","calculateTextBoxWidthMode":"PERCENT","textBoxHeight":146.8,"textBoxWidth":200,"textBoxWidthPercent":50,"textImageSpace":10,"textBoxBorderRadius":0,"textBoxBorderWidth":0,"loadMoreButtonText":"Load More","loadMoreButtonBorderWidth":1,"loadMoreButtonBorderRadius":0,"imageInfoType":"NO_BACKGROUND","itemBorderWidth":1,"itemBorderRadius":0,"itemEnableShadow":false,"itemShadowBlur":20,"itemShadowDirection":135,"itemShadowSize":10,"imageLoadingMode":"BLUR","expandAnimation":"NO_EFFECT","imageQuality":90,"usmToggle":false,"usm_a":0,"usm_r":0,"usm_t":0,"videoSound":false,"videoSpeed":1,"videoLoop":true,"gotStyleParams":true,"selectedLayout":"2|left|1|fill|true|0|true","allowSocial":true,"allowDownload":false,"allowTitle":true,"allowDescription":true,"loveButton":true,"loveCounter":true,"showVideoPlayButton":true,"galleryImageRatio":2,"sharpParams":{"quality":90,"usm":{}},"galleryHorizontalAlign":"center","galleryVerticalAlign":"center","imageLoadingWithColorMode":"PICKED_COLOR","imageRatioType":"FIXED","numberOfDisplayedItems":3,"itemBorderColor":{"themeName":"color_15","value":"rgba(65,65,65,1)"},"itemShadowOpacityAndColor":{"themeName":"color_15","value":"rgba(65,65,65,0.2)"},"textBoxBorderColor":"color-5","titleDescriptionSpace":6,"textsVerticalPadding":0,"textsHorizontalPadding":0,"textBoxFillColor":"color-2","alwaysShowHover":false,"isStoreGallery":false,"previewHover":false,"calculateTextBoxHeightMode":"MANUAL","galleryLayout":2,"useCustomButton":false,"customButtonText":"","galleryImageRatioFromWix":0.75,"itemOpacity":{"themeName":"color_33","value":"rgba(246,149,34,0.8)"},"itemFont":{"style":{"bold":false,"italic":false,"underline":false},"family":"proxima-n-w01-reg","preset":"Heading-L","editorKey":"font_4","size":40,"fontStyleParam":true,"displayName":"Heading 4","value":"font:normal normal normal 40px/1.4em proxima-n-w01-reg,sans-serif;"},"itemFontSlideshow":{"family":"proxima-n-w01-reg","style":{"bold":true,"italic":false,"underline":false},"size":22,"preset":"Custom","editorKey":"font_6","fontStyleParam":true,"value":"font:normal normal bold 22px/27px proxima-n-w01-reg,sans-serif;"},"itemDescriptionFontSlideshow":{"family":"proxima-n-w01-reg","style":{"bold":false,"italic":false,"underline":false},"size":14,"preset":"Body-S","editorKey":"font_9","fontStyleParam":true,"displayName":"Paragraph 3","value":"font:normal normal normal 14px/1.4em proxima-n-w01-reg,sans-serif;"},"itemDescriptionFont":{"family":"avenir-lt-w01_35-light1475496","displayName":"Paragraph 2","style":{"bold":false,"italic":false,"underline":false},"size":15,"preset":"Custom","editorKey":"font_8","fontStyleParam":true,"value":"font:normal normal normal 15px/18px avenir-lt-w01_35-light1475496,sans-serif;"},"itemFontColor":{"themeName":"color_11","value":"rgba(255,255,255,1)"},"itemFontColorSlideshow":{"themeName":"color_15","value":"rgba(65,65,65,1)"},"itemDescriptionFontColor":{"themeName":"color_11","value":"rgba(255,255,255,1)"},"itemDescriptionFontColorSlideshow":{"themeName":"color_15","value":"rgba(65,65,65,1)"},"loadMoreButtonFont":{"family":"worksans-extralight","displayName":"Paragraph 2","style":{"bold":true,"italic":false,"underline":false},"size":16,"preset":"Body-M","editorKey":"font_8","fontStyleParam":true,"value":"font:normal normal bold 16px/1.4em worksans-extralight,\"work sans\",sans-serif;"},"loadMoreButtonFontColor":{"themeName":"color_15","value":"rgba(65,65,65,1)"},"loadMoreButtonColor":{"themeName":"color_11","value":"rgba(255,255,255,1)"},"loadMoreButtonBorderColor":{"themeName":"color_15","value":"rgba(65,65,65,1)"},"arrowsColor":{"themeName":"color_11","value":"rgba(255,255,255,1)"},"oneColorAnimationColor":{"themeName":"color_11","value":"rgba(255,255,255,1)"},"responsive":false,"modifiedGallerySize":true,"isAccessible":false,"allowLeanGallery":false,"layoutsVersion":2,"selectedLayoutV2":2,"isSlideshowFont":true,"externalInfoHeight":146.8,"externalInfoWidth":0},"container":{"top":"","bottom":"","left":"","right":"","width":980,"height":500,"position":"","avoidGallerySelfMeasure":true,"galleryWidth":995,"galleryHeight":500,"scrollBase":0}}

### Test 1 Section 4

You may use a calculator.